Fundamental Constraints on Multicast Capacity Regions
Fundamental Constraints on Multicast Capacity Regions
复制标题
组播容量区域的基本限制
DOI：
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发表时间：
2008
期刊：
影响因子：
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通讯作者：
David Tse
中科院分区：
文献类型：
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作者：
Leonard H. Grokop;David Tse
广播信道上的许多现有工作仅集中在发送私人消息上。在这项工作中，我们研究的情况下，发送者也希望发送共同的消息的接收器的子集。对于L个用户广播信道，有2L - 1个接收机子集和相应的2L - 1个独立消息。该信道的可实现速率的集合是2L - 1维区域。该区域的几何形状存在基本约束。例如，观察到如果发射机能够同时无差错地向所有接收机发送L个速率一专用消息，则通过在每个消息中发送相同的信息，它必须能够无差错地向所有接收机发送单个速率一公共消息。私有消息和公共消息的这种交换说明，对于任何广播信道，在可达到速率区域中包括点R* 意味着不仅仅在分量上小于R* 的一组其他点的可重复性。我们以前定义了这个集合，并对L = 2和L = 3刻画了它。然而，对于L = 2，集合中的所有点仅产生于与交换私有和公共消息相关的操作，对于L = 3，需要网络编码的形式。
Much of the existing work on the broadcast channel focuses only on the sending of private messages. In this work we examine the scenario where the sender also wishes to transmit common messages to subsets of receivers. For an L user broadcast channel there are 2L - 1 subsets of receivers and correspondingly 2L - 1 independent messages. The set of achievable rates for this channel is a 2L - 1 dimensional region. There are fundamental constraints on the geometry of this region. For example, observe that if the transmitter is able to simultaneously send L rate-one private messages, error-free to all receivers, then by sending the same information in each message, it must be able to send a single rate-one common message, error-free to all receivers. This swapping of private and common messages illustrates that for any broadcast channel, the inclusion of a point R* in the achievable rate region implies the achievability of a set of other points that are not merely component-wise less than R*. We formerly define this set and characterize it for L = 2 and L = 3. Whereas for L = 2 all the points in the set arise only from operations relating to swapping private and common messages, for L = 3 a form of network coding is required.